Link Reversal Routing with Binary Link Labels: Work Complexity

Abstract

Full Reversal and Partial Reversal are two well-known routing algorithms that were introduced by Gafni and Bertsekas [IEEE Trans. Commun., 29 (1981), pp. 11--18]. By reversing the directions of some links of the graph, these algorithms transform a connected input DAG (directed acyclic graph) into an output DAG in which each node has at least one path to a distinguished destination node. We present a generalization of these algorithms, called the link reversal (LR) algorithm, based on a novel formalization that assigns binary labels to the links of the input DAG. We characterize the legal link labelings for which LR is guaranteed to establish routes. Moreover, we give an exact expression for the number of steps---called work complexity---taken by each node in every execution of LR from any legal input graph. Exact expressions for the per-node work complexity of Full Reversal and Partial Reversal follow from our general formula; this is the first exact expression known for Partial Reversal. Our binary link ...